The district curriculum guide suggests that we delve into sequences and series. Since there are no required standards, I have the opportunity to structure more exploratory activities in the unit. Students will study the typical sequences and series concepts/skills in their next math course (precalculus).
I borrowed from Jo Boaler's YouCubed Week of Inspirational Math, Henri Picciotto's work, and an NCTM Student Explorations (What Shapes Do You See, Jan 2012) to blend together five exploratory lessons.
- Number Patterns
- Growing Shapes
- Patterns in a Triangle
- Staircase Sums
- Averages and Sums
As we process students' explorations each day, we will address these concepts:
- The difference between an arithmetic and geometric sequence
- The difference between a sequence and a series
- The difference between convergent and divergent series
We will leave the formulas and details for next year's unit.
Today was day 1 ... and it was a lot of fun! I wish I had audio recording or pictures but I don't.
First students completed a short exam review learning check with partners. I loved hearing the buzz in the room as partners convinced one another how to find the solutions asked. (We are reviewing a small set of questions in each class for the next 2 weeks).
Then I gave a brief introduction to our new unit. I gave them copies of the visual numbers from Boaler's lessons. Students got excited when they realized prime numbers were represented by a circle in the visual number display. Other students were stymied at first - one said, "I just see a bunch of little circles." I overhead students arguing over how to represent the number 36.
They did a great job with the consecutive number sums. They caught on quickly when they were allowed to add negative numbers and zero to the patterns.
Only the hundreds' chart patterns slowed them down a bit but it was hilarious to watch light bulbs ignite as they realized the patterns. Then they argued how to write those patterns algebraically.
I am pumped to see what happens in the future lessons! Love that we get to wrap up the year with explorations!